Question: Rewrite as a simplified fraction. ${0.4\overline{76} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 476.7676...\\ 10x &= 4.7676...\end{align*}}$ Subtracting the two equations, we have: ${990x = 472}$ ${x = \dfrac{472}{990}} $ ${x = \dfrac{236}{495}} $